AirDrop is available on iPhone 5 or later, iPad (4th generation), iPad mini, and iPod touch (5th generation) and requires an iCloud account

does Airdrop use wifi or Bluetooth? even in the case if it works with Bluetooth?
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jerremyJan 9 '14 at 18:10

It is WiFi file exchange using an ad-hoc, non router based 802.11 protocol. Think of it as a mesh network that doesn't care whether any of the devices are connected to any or the same WiFI network. I believe bluetooth is only used to negotiate the wireless connection and not transfer files, but I don't have a reference or any facts behind that belief.
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bmike♦Jan 9 '14 at 18:12

While your iPad mini supports AirDrop, the your iPhone 4 does not - and as far as I'm aware, music can't be transferred via AirDrop.

That said, for $25/year, you can turn on iTunes Match, which will put a copy of your iTunes library in iCloud, allowing you to access your music anywhere. You can also transfer the music by using a Mac.

Good answer on iTunes Match. It's less flexible than if you could "beam" a song to another device without being connected to the internet, but it is available today and works quite well for many people's needs.
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bmike♦Jan 9 '14 at 18:13